Model selection based on penalized f-divergences for multinomial data

A test approach to the model selection problem for multinomial data based on penalized phi-divergences is proposed. The test statistic is a sample version of the difference of the distances between the population and each competing model. The null distribution of the test statistic is derived, showing that it depends on whether the competing models intersect or not and whether certain parameter is positive or not. All possible cases are characterized, and we give rules to decide if a model provides a better explanation for the available data than the other. The practical behavior of the proposal is evaluated by means of an extensive simulation experiment. The method is applied to a real data set related to the classification of individuals according to their social preferences. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study proposes a test approach based on penalized phi-divergences to address the model selection problem for multinomial data. By deriving the null distribution and providing decision rules, it is possible to determine which model better explains the available data. The practical behavior of the approach is evaluated through simulation experiments and applied to a real data set related to social preference classification.